Entropy

Arcsine distribution differential entropy.

The differential entropy (in nats) for an arcsine random variable with minimum support a and maximum support b is

h left-parenthesis upper X right-parenthesis equals ln StartFraction pi Over 4 EndFraction

Usage

var entropy = require( '@stdlib/math/base/dists/arcsine/entropy' );

entropy( a, b )

Returns the differential entropy of an arcsine distribution with minimum support a and maximum support b (in nats).

var v = entropy( 0.0, 1.0 );
// returns ~-0.242

v = entropy( 4.0, 12.0 );
// returns ~1.838

v = entropy( 2.0, 8.0 );
// returns ~1.55

If provided NaN as any argument, the function returns NaN.

var v = entropy( NaN, 2.0 );
// returns NaN

v = entropy( 2.0, NaN );
// returns NaN

If provided a >= b, the function returns NaN.

var y = entropy( 3.0, 2.0 );
// returns NaN

y = entropy( 3.0, 3.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var entropy = require( '@stdlib/math/base/dists/arcsine/entropy' );

var a;
var b;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    a = ( randu()*10.0 );
    b = ( randu()*10.0 ) + a;
    v = entropy( a, b );
    console.log( 'a: %d, b: %d, h(X;a,b): %d', a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}